Examsnet
Unconfined exams practice
Home
Exams
Banking Entrance Exams
CUET Exam Papers
Defence Exams
Engineering Exams
Finance Entrance Exams
GATE Exam Practice
Insurance Exams
International Exams
JEE Exams
LAW Entrance Exams
MBA Entrance Exams
MCA Entrance Exams
Medical Entrance Exams
Other Entrance Exams
Police Exams
Public Service Commission (PSC)
RRB Entrance Exams
SSC Exams
State Govt Exams
Subjectwise Practice
Teacher Exams
SET Exams(State Eligibility Test)
UPSC Entrance Exams
Aptitude
Algebra and Higher Mathematics
Arithmetic
Commercial Mathematics
Data Based Mathematics
Geometry and Mensuration
Number System and Numeracy
Problem Solving
Board Exams
Andhra
Bihar
CBSE
Gujarat
Haryana
ICSE
Jammu and Kashmir
Karnataka
Kerala
Madhya Pradesh
Maharashtra
Odisha
Tamil Nadu
Telangana
Uttar Pradesh
English
Competitive English
Certifications
Technical
Cloud Tech Certifications
Security Tech Certifications
Management
IT Infrastructure
More
About
Careers
Contact Us
Our Apps
Privacy
Test Index
JEE Advanced 2018 Paper 2
Show Para
Hide Para
Share question:
© examsnet.com
Question : 38
Total: 54
Let T be the line passing through the points
P
(
−
2
,
7
)
and
Q
(
2
,
−
5
)
.Let
F
1
be the set of all pairs of circles
(
S
1
,
S
2
)
such that T is tangents to
S
1
at P and tangent to
S
2
at Q, and also such that
S
1
and
S
2
touch each other at a point, say, M. Let
E
1
be the set representing the locus of M as the pair
(
S
1
,
S
2
)
varies in
F
1
. Let the set of all straight line segments joining a pair of distinct points of
E
1
and passing through the point R(1, 1) be
F
2
.Let
F
2
be the set of the mid-points of the line segments in the set
F
2
.Then, which of the following statements(s) is (are) TRUE?
The point
(
−
2
,
7
)
lies in
E
1
The point
(
4
5
,
7
5
)
does NOT lie in
E
2
The point
(
1
2
,
1
)
lies in
E
2
The point
(
0
,
3
2
)
does NOT lie in
E
1
Validate
Solution:
A
P
=
A
Q
=
A
M
Locus of M is a circle having PQ as its diameter
Hence,
E
1
:
(
x
−
2
)
(
x
+
2
)
+
(
y
−
7
)
(
y
+
5
)
=
0
and
x
≠
±
2
Locus of B (midpoint) is a circle having RC as its diameter
E
2
:
x
(
x
−
1
)
+
(
y
−
1
)
2
=
0
Now, after checking the options, we get (D)
© examsnet.com
Go to Question:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
Prev Question
Next Question